“You Know My Name (Look Up the Number)” is pretty much the Beatles riffing on the Goons. (See also their 1966 and 1967 Christmas fan club recordings.)
One of my Rules is ‘Never analyse why comedy is funny’ - so here goes.
I think an important thing to remember is that by the time Python was formed, they were already all successful comedy writers and performers. They had all been on David Frost in some form or other (that was Comedy Royalty in Early 60s Britain), Cleese and Chapman had written a few series of Doctor In The House - about as twee and harmelss a sitcom as you can get, they had had some TV sucess with History of Britain and 1948, and had written for and appeared on numerous Radio comedies. They worked with the guys who formed the Goodies, The two Ronnies, Eric Sykes, Frankie Howerd, Martry Feldman, they worked with David Hatch who became BBC Head of Comedy - they were in the Modern Comedy Establishment.
So they weren’t struggling comedians trying to make a big, controversial impact - they were seasoned performers who decided to try and do something different and excellent rather than just coast along and draw comfortable pay packets. As some have mentioned here, they tried to break down what it was that was funny - and then take that magic ingredient and apply it. A form of meta-comedy - don’t apply comedy to a situation - make the comedy itself funny (I’m not explaining myself very well here).
They mention they were strongly influenced by Spike Milligan - particularly, at the time, by his Q5 TV series. No formula, no punchlines (except those described as punchlines - one of his staples was to have characters walking off-stage zombie-like, repeating ‘What are we going to do now’) etc. What Milligan had done was not write funny sketches about various situatiosn - he had written funny sketches about comedy sketches about situations.
Actually, just re-read the first line of this post.